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it is line set out by the optical axis of the instrument ( level). so it is just an imaginary line that describes the ray of light that allowes us to read different values from the leveling staff. this term arose from the fact that in differential leveling in surveying we must construct horizontal line of sight, but due to collimation error the collimation line (i.e. line of sight) will not be 100% horizontal (by horizontal we mean tangent the level surface at the instrument position), instead it will be slightly deviated. so what we are looking to achieve when we eliminate the collimation error (using the 2 peg test) is a horizontal line of collimation.
Transit and non-transit theodolite.
A theodolite is used to measure angles of a plane. This can be both vertical or horizontal, and it is used with high precision.
20 degree
upper clamb